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Simplifying 100x + -1x2 = 576 Solving 100x + -1x2 = 576 Solving for variable 'x'. Reorder the terms: -576 + 100x + -1x2 = 576 + -576 Combine like terms: 576 + -576 = 0 -576 + 100x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 576 + -100x + x2 = 0 Move the constant term to the right: Add '-576' to each side of the equation. 576 + -100x + -576 + x2 = 0 + -576 Reorder the terms: 576 + -576 + -100x + x2 = 0 + -576 Combine like terms: 576 + -576 = 0 0 + -100x + x2 = 0 + -576 -100x + x2 = 0 + -576 Combine like terms: 0 + -576 = -576 -100x + x2 = -576 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -576 + 2500 Reorder the terms: 2500 + -100x + x2 = -576 + 2500 Combine like terms: -576 + 2500 = 1924 2500 + -100x + x2 = 1924 Factor a perfect square on the left side: (x + -50)(x + -50) = 1924 Calculate the square root of the right side: 43.863424399 Break this problem into two subproblems by setting (x + -50) equal to 43.863424399 and -43.863424399.Subproblem 1
x + -50 = 43.863424399 Simplifying x + -50 = 43.863424399 Reorder the terms: -50 + x = 43.863424399 Solving -50 + x = 43.863424399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 43.863424399 + 50 Combine like terms: -50 + 50 = 0 0 + x = 43.863424399 + 50 x = 43.863424399 + 50 Combine like terms: 43.863424399 + 50 = 93.863424399 x = 93.863424399 Simplifying x = 93.863424399Subproblem 2
x + -50 = -43.863424399 Simplifying x + -50 = -43.863424399 Reorder the terms: -50 + x = -43.863424399 Solving -50 + x = -43.863424399 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -43.863424399 + 50 Combine like terms: -50 + 50 = 0 0 + x = -43.863424399 + 50 x = -43.863424399 + 50 Combine like terms: -43.863424399 + 50 = 6.136575601 x = 6.136575601 Simplifying x = 6.136575601Solution
The solution to the problem is based on the solutions from the subproblems. x = {93.863424399, 6.136575601}
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